An Arbitrage‐Free Estimate of Prepayment Option Prices in Fixed‐Rate GNMA Mortgage‐Backed Securities

Abstract

In an efficient market, the no-arbitrage condition implies that the price difference between any two assets must be the market value of all differences in their cash flows. We use this logic to deduce the price of the prepayment option embedded in fixed-rate Government National Mortgage Association (GNMA) mortgage-backed securities. The option price equals the difference between an observed GNMA price and the cost of a synthetic, nonprepayable GNMA constructed from the least expensive portfolio of Treasury securities that exactly replicates the promised GNMA cash flow stream, assuming prepayment is precluded. We regress the option prices on variables found significant in previous prepayment studies, finding that five key regressors explain more than 90% of the prepayment option value in pooled time-series cross-sectional analysis. We also show that the time value of the prepayment option calculated by our method displays a pattern similar to that produced by the Black-Scholes (1973) option pricing model. An additional empirical result is the existence of negative option prices and negative time value of the option prices. We attribute these to the fact that homeowners sometimes exercise their prepayment options when they are out-of-the-money, and to refinancing transaction costs. Our method is independent of assumptions regarding interest rate processes and the homeowner's prepayment behavior, and it provides a benchmark for testing theoretical prepayment models. Copyright American Real Estate and Urban Economics Association.

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“…The research on individual borrower characteristics in transaction-based loan samples show that family size, education, age of household head (Canner and Luckett, 1990), interest rate (Green and Shoven, 1986), interest rate volatility and household income affect prepayment (Giliberto and Thibodeau, 1989;Dickinson and Heuson, 1992). In particular, Dickinson and Heuson (1992) show that increases in income and house values or decreases in interest rates Cox et al (1980), the level of interest rate is also used as a proxy for interest rate volatility in the study of prepayment (Ronn et al, 1995).…”